View source for Measurable space

{{Refactor notice|grade=A*|msg=Lets get this measure theory stuff sorted. At least the skeleton
* I can probably remove the old page... it doesn't say anything different.}}
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==Definition==
Given a [[set]], {{M|X}}, and a [[sigma-algebra|{{sigma|algebra}}]], {{M|\mathcal{A}\in\mathcal{P}(\mathcal{P}(X))}}<ref group="Note">More neatly written perhaps:
* {{M|A\subseteq\mathcal{P}(X)}}</ref> then a ''measurable space''{{rMIAMRLS}}{{rAGTARAF}} is the [[tuple]]:
* {{M|(X,\mathcal{A})}}
This is not to be confused with a ''[[measure space]]'' which is a [[tuple|{{M|3}}-tuple]]: {{M|(X,\mathcal{A},\mu)}} where {{M|\mu}} is a [[measure]] on the ''measurable space'' {{M|(X,\mathcal{A})}}
===[[Premeasurable space]]===
{{:Premeasurable space/Definition}}
==See also==
* [[Pre-measurable space]]
* [[Measure space]]
** [[Measure]]
** [[Measurable map]]
==Notes==
<references group="Note"/>
==References==
<references/>
{{Definition|Measure Theory}}


=OLD PAGE=
==Definition==
A ''measurable space''<ref name="MIM">Measures, Integrals and Martingales - Rene L. Schilling</ref> is a [[Tuple|tuple]] consisting of a set {{M|X}} and a [[Sigma-algebra|{{Sigma|algebra}}]] {{M|\mathcal{A} }}, which we denote:
* {{M|(X,\mathcal{A})}}
==Pre-measurable space==
A ''pre-measurable space''<ref name="ALEC">Alec's own terminology, it's probably not in books because it's barely worth a footnote</ref> is a set {{M|X}} coupled with an [[Algebra of sets|algebra]], {{M|\mathcal{A} }} (where {{M|\mathcal{A} }} is '''NOT''' a {{sigma|algebra}}) which we denote as follows:
* {{M|(X,\mathcal{A})}}
==See also==
* [[Pre-measure space]]
* [[Measure space]]
* [[Measurable map]]

==References==
<references/>

{{Definition|Measure Theory}}